To evaluate the limit of $e^x$ as $x$ approaches 1, we simply substitute $x = 1$ directly into the expression, since $e^x$ is a continuous function.

$\lim_{x \to 1} e^x = e^1 = e$

Thus, the limit is $e$, which is approximately 2.718.

Let me know if you'd like further details on this, or if you have any more questions!

Here are some related questions to consider:

1. What happens to $\lim_{x \to 0} e^x$?
2. How do you prove the continuity of $e^x$?
3. What is the derivative of $e^x$?
4. How does the exponential function $e^x$ behave as $x \to \infty$?
5. What are the limits involving $e^x$ at other points, like 0 or -1?

Tip: Exponential functions like $e^x$ are continuous everywhere, meaning you can often directly substitute values into the function when evaluating limits.